How to stop Blender from simulating smoke when doing some things
Bake the simulation to a cache, then blender doesn't need to recalculate the simulation.

In order to bake the cache, you must save your blend file first, otherwise the buttons will be greyed out.

Read more in the blender manual section on baking smoke.

You won't need to hide the domain after you do this, unless of course you don't want to see it.